Eur. Phys. J. C (2017) 77:241
DOI 10.1140/epjc/s10052-017-4780-2
Regular Article - Experimental Physics
Performance of algorithms that reconstruct missing transverse
momentum in
√
s = 8 TeV proton–proton collisions in the ATLAS
detector
ATLAS Collaboration
CERN, 1211 Geneva 23, Switzerland
Received: 30 September 2016 / Accepted: 21 March 2017 / Published online: 13 April 2017
© CERN for the benefit of the ATLAS collaboration 2017. This article is an open access publication
Abstract The reconstruction and calibration algorithms
used to calculate missing transverse momentum (E
miss
T
) with
the ATLAS detector exploit energy deposits in the calorime-
ter and tracks reconstructed in the inner detector as well as
the muon spectrometer. Various strategies are used to sup-
press effects arising from additional proton–proton interac-
tions, called pileup, concurrent with the hard-scatter pro-
cesses. Tracking information is used to distinguish contribu-
tions from the pileup interactions using their vertex separa-
tion along the beam axis. The performance of the E
miss
T
recon-
struction algorithms, especially with respect to the amount
of pileup, is evaluated using data collected in proton–proton
collisions at a centre-of-mass energy of 8 TeV during 2012,
and results are shown for a data sample corresponding to
an integrated luminosity of 20.3fb
−1
. The simulation and
modelling of E
miss
T
in events containing a Z boson decaying
to two charged leptons (electrons or muons) or a W boson
decaying to a charged lepton and a neutrino are compared
to data. The acceptance for different event topologies, with
and without high transverse momentum neutrinos, is shown
for a range of threshold criteria for E
miss
T
, and estimates of
the systematic uncertainties in the E
miss
T
measurements are
presented.
Contents
1 Introduction ..................... 2
2 ATLAS detector ................... 2
3 Data samples and event selection .......... 3
3.1 Track and vertex selection ............ 3
3.2 Event selection for Z → ........... 4
3.3 Event selection for W → ν .......... 4
3.4 Monte Carlo simulation samples ........ 5
4 Reconstruction and calibration of the E
miss
T
..... 6
4.1 Reconstruction of the E
miss
T
........... 6
e-mail:
atlas.publications@cern.ch
4.1.1 Reconstruction andcalibrationofthe E
miss
T
hard terms
................. 6
4.1.2 Reconstruction andcalibrationofthe E
miss
T
soft
term
.................... 7
4.1.3 Jet p
T
threshold and JVF selection ...10
4.2 Track E
miss
T
................... 11
5 Comparison of E
miss
T
distributions in data and MC
simulation
...................... 11
5.1 Modelling of Z → events .......... 11
5.2 Modelling of W → ν events ......... 14
6 Performance of the E
miss
T
in data and MC simulation 14
6.1 Resolution of E
miss
T
............... 14
6.1.1 Resolution of the E
miss
T
as a function of
the number of reconstructed vertices
... 15
6.1.2 Resolution of the E
miss
T
as a function of E
T
16
6.2 The E
miss
T
response ............... 17
6.2.1 Measuring E
miss
T
recoil versus p
Z
T
.... 17
6.2.2 Measuring E
miss
T
response in simulated
W → ν events
............. 18
6.3 The
E
miss
T
angular resolution .......... 19
6.4 Transverse mass in W → ν events ...... 19
6.5 Proxy for E
miss
T
significance .......... 20
6.6 Tails of E
miss
T
distributions ........... 21
6.7 Correlation of fake E
miss
T
between algorithms .23
7Jet-p
T
threshold and vertex association selection .. 24
8 Systematic uncertainties of the soft term ...... 25
8.1 Methodology for CST .............. 25
8.1.1 Evaluation of balance between the soft
term and the hard term .......... 25
8.1.2 Cross-check method for the CST system-
atic uncertainties ............. 26
8.2 Methodology for TST and Track E
miss
T
..... 26
8.2.1 Propagation of systematic uncertainties .28
8.2.2 Closure of systematic uncertainties .... 29
8.2.3 Systematic uncertainties fromtracksinside
jets
.................... 30
9 Conclusions ..................... 31
123
241 Page 2 of 46 Eur. Phys. J. C (2017) 77 :241
Appendix ........................ 32
A. Calculation of EJAF ................. 32
References ........................ 32
1 Introduction
The Large Hadron Collider (LHC) provided proton–proton
(pp) collisions at a centre-of-mass energy of 8 TeV during
2012. Momentum conservation transverse to the beam axis
1
implies that the transverse momenta of all particles in the
final state should sum to zero. Any imbalance may indicate
the presence of undetectable particles such as neutrinos or
new, stable particles escaping detection.
The missing transverse momentum (
E
miss
T
) is recon-
structed as the negativevectorsum of the transverse momenta
( p
T
) of all detected particles, and its magnitude is represented
by the symbol E
miss
T
. The measurement of E
miss
T
strongly
depends on the energy scale and resolution of the recon-
structed “physics objects”. The physics objects considered
in the E
miss
T
calculation are electrons, photons, muons, τ -
leptons, and jets. Momentum contributions not attributed to
any of the physics objects mentioned above are reconstructed
as the E
miss
T
“soft term”. Several algorithms for reconstruct-
ing the E
miss
T
soft term utilizing a combination of calorimeter
signals and tracks in the inner detector are considered.
The E
miss
T
reconstruction algorithms and calibrations
developed by ATLAS for 7 TeV data from 2010 are sum-
marized in Ref. [
1]. The 2011 and 2012 datasets are more
affected by contributions from additional pp collisions,
referred to as “pileup”, concurrent with the hard-scatter pro-
cess. Various techniques have been developed to suppress
such contributions. This paper describes the pileup depen-
dence, calibration, and resolution of the E
miss
T
reconstructed
with different algorithms and pileup-mitigation techniques.
The performance of E
miss
T
reconstruction algorithms, or
“E
miss
T
performance”, refers to the use of derived quanti-
ties like the mean, width, or tail of the E
miss
T
distribution to
study pileup dependence and calibration. The E
miss
T
recon-
structed with different algorithms is studied in both data and
Monte Carlo (MC) simulation, and the level of agreement
between the two is compared using datasets in which events
with a leptonically decaying W or Z boson dominate. The W
boson sample provides events with intrinsic E
miss
T
from non-
interacting particles (e.g. neutrinos). Contributions to the
E
miss
T
due to mismeasurement are referred to as fake E
miss
T
.
1
ATLAS uses a right-handed coordinate system with its origin at the
nominal interaction point (IP) in the centre of the detector and the z-axis
along the beam pipe. The x-axis points from the IP to the centre of the
LHC ring, and the y-axis points upward. Cylindrical coordinates (r,φ)
are used in the transverse plane, φ being the azimuthal angle around the
beam pipe. The pseudorapidity is defined in terms of the polar angle θ
as η =−ln tan(θ/2).
Sources of fake E
miss
T
may include p
T
mismeasurement,
miscalibration, and particles going through un-instrumented
regions of the detector. In MC simulations, the E
miss
T
from
each algorithm is compared to the true E
miss
T
(E
miss,True
T
),
which is defined as the magnitude of the vector sum of p
T
of
stable
2
weakly interacting particles from the hard-scatter col-
lision. Then the selection efficiency after a E
miss
T
-threshold
requirement is studied in simulated events with high-p
T
neu-
trinos (such as top-quark pair production and vector-boson
fusion H → ττ) or possible new weakly interacting particles
that escape detection (such as the lightest supersymmetric
particles).
This paper is organized as follows. Section
2 gives a brief
introduction to the ATLAS detector. Section
3 describes the
data and MC simulation used as well as the event selections
applied. Section
4 outlines how the E
miss
T
is reconstructed
and calibrated while Sect.
5 presents the level of agreement
between data and MC simulation in W and Z boson produc-
tion events. Performance studies of the E
miss
T
algorithms on
data and MC simulation are shown for samples with different
event topologies in Sect.
6. The choice of jet selection crite-
ria used in the E
miss
T
reconstruction is discussed in Sect.
7.
Finally, the systematic uncertainty in the absolute scale and
resolution of the E
miss
T
is discussed in Sect.
8. To provide
a reference, Table
1 summarizes the different E
miss
T
terms
discussed in this paper.
2 ATLAS detector
The ATLAS detector [
2] is a multi-purpose particle physics
apparatus with a forward-backward symmetric cylindrical
geometry and nearly 4π coverage in solid angle. For track-
ing, the inner detector (ID) covers the pseudorapidity range
of |η| < 2.5, and consists of a silicon-based pixel detector,
a semiconductor tracker (SCT) based on microstrip technol-
ogy, and, for |η| < 2.0, a transition radiation tracker (TRT).
The ID is surrounded by a thin superconducting solenoid pro-
viding a 2 T magnetic field, which allows the measurement
of the momenta of charged particles. A high-granularity elec-
tromagnetic sampling calorimeter based on lead and liquid
argon (LAr) technology covers the region of |η| < 3.2. A
hadronic calorimeter based on steel absorbers and plastic-
scintillator tiles provides coverage for hadrons, jets, and τ -
leptons in the range of |η| < 1.7. LAr technology using a
copper absorber is also used for the hadronic calorimeters in
the end-cap region of 1.5 < |η| < 3.2 and for electromag-
netic and hadronic measurements with copper and tungsten
absorbing materials in the forward region of 3.1 < |η| < 4.9.
The muon spectrometer (MS) surrounds the calorimeters. It
2
ATLAS defines stable particles as those having a mean lifetime >
0.3 ×10
−10
s.
123
Eur. Phys. J. C (2017) 77 :241 Page 3 of 46 241
Tab l e 1 Summary of definitions for E
miss
T
termsusedinthispaper
Term Brief description
Intrinsic E
miss
T
Missing transverse momentum arising from the presence of neutrinos or other non-interacting particles in
an event. In case of simulated events the true E
miss
T
(E
miss,True
T
) corresponds to the E
miss
T
in such events
defined as the magnitude of the vector sum of p
T
of non-interacting particles computed from the
generator information
Fake E
miss
T
Missing transverse momentum arising from the miscalibration or misidentification of physics objects in
the event. It is typically studied in Z → μμ events where the intrinsic E
miss
T
is normally expected to be
zero
Hard terms The component of the E
miss
T
computed from high-p
T
physics objects, which includes reconstructed
electrons, photons, muons, τ -leptons, and jets
Soft terms Typically low-p
T
calorimeter energy deposits or tracks, depending on the soft-term definition, that are not
associated to physics objects included in the hard terms
Pileup-suppressed E
miss
T
All E
miss
T
reconstruction algorithms in Sect.
4.1.2 except the Calorimeter Soft Term, which does not apply
pileup suppression
Object-based This refers to all reconstruction algorithms in Sect.
4.1.2 except the Track E
miss
T
, namely the Calorimeter
Soft Term, Track Soft Term, Extrapolated Jet Area with Filter, and Soft-Term Vertex-Fraction
algorithms. These consider the physics objects such as electrons, photons, muons, τ -leptons, and jets
during the E
miss
T
reconstruction
consists of three air-core superconducting toroid magnet sys-
tems, precision tracking chambers to provide accurate muon
tracking out to |η|=2.7, and additional detectors for trig-
gering in the region of |η| < 2.4. A precision measurement
of the track coordinates is provided by layers of drift tubes at
three radial positions within |η| < 2.0. For 2.0 < |η| < 2.7,
cathode-strip chambers with high granularity are instead used
in the innermost plane. The muon trigger system consists of
resistive-plate chambers in the barrel (|η| < 1.05) and thin-
gap chambers in the end-cap regions (1.05 < |η| < 2.4).
3 Data samples and event selection
ATLAS recorded pp collisions at a centre-of-mass energy of
8 TeV with a bunch crossing interval (bunch spacing) of 50 ns
in 2012. The resulting integrated luminosity is 20.3fb
−1
[
3].
Multiple inelastic pp interactions occurred in each bunch
crossing, and the mean number of inelastic collisions per
bunch crossing (μ) over the full dataset is 21 [
4], excep-
tionally reaching as high as about 70.
Data are analysed only if they satisfy the standard ATLAS
data-quality assessment criteria [
5]. Jet-cleaning cuts [5]are
applied to minimize the impact of instrumental noise and out-
of-time energy deposits in the calorimeter from cosmic rays
or beam-induced backgrounds. This ensures that the residual
sources of E
miss
T
mismeasurement due to those instrumental
effects are suppressed.
3.1 Track and vertex selection
The ATLASdetector measures the momenta of charged parti-
cles using the ID [
6]. Hits from charged particles are recorded
and are used to reconstruct tracks; these are used to recon-
struct vertices [
7,8].
Each vertex must have at least two tracks with p
T
>
0.4 GeV; for the primary hard-scatter vertex (PV), the
requirement on the number of tracks is raised to three. The
PV in each event is selected as the vertex with the largest
value of (p
T
)
2
, where the scalar sum is taken over all the
tracks matched to the vertex. The following track selection
criteria
3
[7] are used throughout this paper, including the
vertex reconstruction:
• p
T
> 0.5 GeV (0.4 GeV for vertex reconstruction and the
calorimeter soft term),
•|η| < 2.5,
• Number of hits in the pixel detector ≥ 1,
• Number of hits in the SCT ≥ 6.
These tracks are then matched to the PV by applying the
following selections:
•|d
0
| < 1.5 mm,
•|z
0
sin(θ )| < 1.5 mm.
The transverse (longitudinal) impact parameter d
0
(z
0
) is
the transverse (longitudinal) distance of the track from the
PV and is computed at the point of closest approach to the
PV in the plane transverse to the beam axis. The require-
ments on the number of hits ensures that the track has an
3
The track reconstruction for electrons and for muons does not strictly
follow these definitions. For example, a Gaussian Sum Filter [
9] algo-
rithm is used for electrons to improve the measurements of its track
parameters, which can be degraded due to Bremsstrahlung losses.
123
241 Page 4 of 46 Eur. Phys. J. C (2017) 77 :241
accurate p
T
measurement. The |η| requirement keeps only
the tracks within the ID acceptance, and the requirement of
p
T
> 0.4 GeV ensures that the track reaches the outer layers
of the I D. Tracks with low p
T
have large curvature and are
more susceptible to multiple scattering.
The average spread along the beamline direction for pp
collisions in ATLAS during 2012 data taking is around
50 mm, and the typical track z
0
resolution for those with
|η| < 0.2 and 0.5 < p
T
< 0.6 GeV is 0.34 mm. The
typical track d
0
resolution is around 0.19 mm for the same η
and p
T
ranges, and both the z
0
and d
0
resolutions improve
with higher track p
T
.
Pileup effects come from two sources: in-time and out-of-
time. In-time pileup is the result of multiple pp interactions
in the same LHC bunch crossing. It is possible to distinguish
the in-time pileup interactions by using their vertex posi-
tions, which are spread along the beam axis. At μ=21,
the efficiency to reconstruct and select the correct vertex for
Z → μμ simulated events is around 93.5% and rises to more
than 98% when requiring two generated muons with p
T
> 10
GeV inside the ID acceptance [
10]. When vertices are sepa-
rated along the beam axis by a distance smaller than the posi-
tion resolution, they can be reconstructed as a single vertex.
Each track in the reconstructed vertex is assigned a weight
based upon its compatibility with the fitted vertex, which
depends on the χ
2
of the fit. The fraction of Z → μμ recon-
structed vertices with more than 50% of the sum of track
weights coming from pileup interactions is around 3% at
μ=21 [
7,10]. Out-of-time pileup comes from pp colli-
sions in earlier and later bunch crossings, which leave signals
in the calorimeters that can take up to 450 ns for the charge
collection time. This is longer than the 50 ns between subse-
quent collisions and occurs because the integration time of
the calorimeters is significantly larger than the time between
the bunch crossings. By contrast the charge collection time
of the silicon tracker is less than 25 ns.
3.2 Event selection for Z →
The “standard candle” for evaluation of the E
miss
T
perfor-
mance is Z → events ( = e or μ). They are produced
without neutrinos, apart from a very small number originat-
ing from heavy-flavour decays in jets produced in association
with the Z boson. The intrinsic E
miss
T
is therefore expected
to be close to zero, and the E
miss
T
distributions are used to
evaluate the modelling of the effects that give rise to fake
E
miss
T
.
Candidate Z → events are required to pass an elec-
tron or muon trigger [
11,12]. The lowest p
T
threshold for the
unprescaled single-electron (single-muon) trigger is p
T
> 25
(24) GeV, and both triggers apply a track-based isolation as
well as quality selection criteria for the particle identifica-
tion. Triggers with higher p
T
thresholds, without the isola-
tion requirements, are used to improve acceptance at high
p
T
. These triggers require p
T
> 60 (36) GeV for electrons
(muons). Events are accepted if they pass any of the above
trigger criteria. Each event must contain at least one primary
vertex with a z displacement from the nominal pp interaction
point of less than 200 mm and with at least three associated
tracks.
The offline selection of Z → μμ events requires the
presence of exactly two identified muons [
13]. An identi-
fied muon is reconstructed in the MS and is matched to
a track in the ID. The combined ID+MS track must have
p
T
> 25 GeV and |η| < 2.5. The z displacement of the
muon track from the primary vertex is required to be less
than 10 mm. An isolation criterion is applied to the muon
track, where the scalar sum of the p
T
of additional tracks
within a cone of size R =
(η)
2
+ (φ)
2
= 0.2 around
the muon is required to be less than 10% of the muon
p
T
. In addition, the two leptons are required to have oppo-
site charge, and the reconstructed dilepton invariant mass,
m
, is required to be consistent with the Z boson mass:
66 < m
< 116 GeV.
The E
miss
T
modelling and performance results obtained in
Z → μμ and Z → ee events are very similar. For the sake
of brevity, only the Z → μμ distributions are shown in all
sections except for Sect.
6.6.
3.3 Event selection for W → ν
Leptonically decaying W bosons (W → ν) provide an
important event topology with intrinsic E
miss
T
;theE
miss
T
distribution for such events is presented in Sect.
5.2.Sim-
ilar to Z → events, a sample dominated by leptoni-
cally decaying W bosons is used to study the E
miss
T
scale in
Sect.
6.2.2, the resolution of the E
miss
T
direction in Sect. 6.3,
and the impact on a reconstructed kinematic observable in
Sect.
6.4.
The E
miss
T
distributions for W boson events in Sect.
5.2
use the electron final state. These electrons are selected with
|η| < 2.47, are required to meet the “medium” identification
criteria [
14] and satisfy p
T
> 25 GeV. Electron candidates in
the region 1.37 < |η| < 1.52 suffer from degraded momen-
tum resolution and particle identification due to the transi-
tion from the barrel to the end-cap detector and are therefore
discarded in these studies. The electrons are required to be
isolated, such that the sum of the energy in the calorime-
ter within a cone of size R = 0.3 around the electron is
less than 14% of the electron p
T
. The summed p
T
of other
tracks within the same cone is required to be less than 7%
of the electron p
T
. The calorimeter isolation variable [
14]
is corrected by subtracting estimated contributions from the
electron itself, the underlying event [
15], and pileup. The
123
Eur. Phys. J. C (2017) 77 :241 Page 5 of 46 241
Tab l e 2 Generators, cross-section normalizations, PDF sets, and MC tunes used in this analysis
Sample Generator Use Cross-section PDF set Tune
Z → μμ Alpgen+Pythia Signal NNLO [26] CTEQ6L1 [27] PERUGIA2011C [18]
Z → ee Alpgen+Pythia Signal NNLO [
26] CTEQ6L1 PERUGIA2011C
Z → ττ Alpgen+Herwig Signal NNLO [26] CTEQ6L1 AUET2 [21]
W → μν Alpgen+Pythia Signal NNLO [
26] CTEQ6L1 PERUGIA2011C
W → eν Alpgen+Pythia Signal NNLO [
26] CTEQ6L1 PERUGIA2011C
W → τν Alpgen+Pythia Signal NNLO [
26] CTEQ6L1 PERUGIA2011C
t
¯
t Powheg+Pythia Signal/background NNLO+NNLL [28,29] CTEQ6L1 PERUGIA2011C
VBF H → ττ Powheg+Pythia8 Signal – NLO CT10 [
30]AU2[31]
SUSY 500 Herwig++ Signal – CTEQ6L1 UE EE3 [
32]
W
±
Z →
±
ν
+
−
Sherpa Background NLO [
33,34]NLOCT10Sherpa default
ZZ →
+
−
ν ¯ν Sherpa Background NLO [
33,34]NLOCT10Sherpa default
W
+
W
−
→
+
ν
−
¯ν Sherpa Background NLO [
33,34]NLOCT10Sherpa default
tW Powheg+Pythia Background NNLO+NNLL [
35] CTEQ6L1 PERUGIA2011C
Z → μμ Powheg+Pythia8 Systematic effects NNLO [
36,37]NLOCT10AU2
Z → μμ Alpgen+Herwig Systematic effects NNLO [
36,37] CTEQ6L1 AUET2
Z → μμ Sherpa Systematic effects NNLO [36,37]NLOCT10Sherpa default
electron tracks are then matched to the PV by applying the
following selections:
•|d
0
| < 5.0 mm,
•|z
0
sin(θ )| < 0.5 mm.
The W boson selection is based on the single-lepton trig-
gers and the same lepton selection criteria as those used in the
Z → selection. Events are rejected if they contain more
than one reconstructed lepton. Selections on the E
miss
T
and
transversemass (m
T
) are applied to reduce the multi-jet back-
ground with one jet misidentified as an isolated lepton. The
transverse mass is calculated from the lepton and the
E
miss
T
,
m
T
=
2p
T
E
miss
T
(1 − cos φ), (1)
where p
T
is the transverse momentum of the lepton and φ is
the azimuthal angle between the lepton and
E
miss
T
directions.
Both the m
T
and E
miss
T
are required to be greater than 50 GeV.
These selections can bias the event topology and its phase
space, so they are only used when comparing simulation to
data in Sect.
5.2, as they substantially improve the purity of
W bosons in data events.
The E
miss
T
modelling and performance results obtained in
W → eν and W → μν events are very similar. For the sake
of brevity, only one of the two is considered in following two
sections: E
miss
T
distributions in W → eν events are presented
in Sect.
5.2 and the performance studies show W → μν
events in Sect.
6. When studying the E
miss
T
tails, both final
states are considered in Sect.
6.6, because the η-coverage
and reconstruction performance between muons and elec-
trons differ.
3.4 Monte Carlo simulation samples
Table
2 summarizes the MC simulation samples used in this
paper. The Z → and W → ν samples are generated with
Alpgen [
16] interfaced with Pythia [17] (denoted by Alp-
gen+Pythia) tomodeltheparton showerandhadronization,
and underlying event using the PERUGIA2011C set [
18]of
tunable parameters. One exception is the Z → ττ sample
with leptonicallydecayingτ -leptons,whichis generated with
Alpgen interfaced with Herwig [
19] with the underlying
event modelled using Jimmy [
20] and the AUET2 tunes [21].
Alpgen is a multi-leg generator that provides tree-level cal-
culations for diagrams with up to five additional partons.
The matrix-element MC calculations are matched to a model
of the parton shower, underlying event and hadronization.
The main processes that are backgrounds to Z → and
W → ν are events with one or more top quarks (t
¯
t and
single-top-quark processes) and diboson production (WW,
WZ, ZZ). The t
¯
t and tW processes are generated with
Powheg [
22] interfaced with Pythia [17] for hadronization
and parton showering, and PERUGIA2011C for the underly-
ing event modelling. All the diboson processes are generated
with Sherpa [
23].
Powheg is a leading-order generator with
corrections at next-to-leading order in α
S
, whereas Sherpa
is a multi-leg generator at tree level.
To study event topologies with high jet multiplicities and
to investigate the tails of the E
miss
T
distributions, t
¯
t events
123